Water reservoir

The water reservoir is filled through one inlet 4 hours later than both together, then another inlet 9 hours later than both together. For how long is filled by each separately?

Correct result:

a =  10 h
b =  15 h

Solution:

$$\begin{gathered} {\displaystyle \frac{1}{a}}+{\displaystyle \frac{1}{b}}={\displaystyle \frac{1}{s}} \\ s={\displaystyle \frac{ab}{a+b}} \\ a=4+s \\ b=9+s \\ a=4+{\displaystyle \frac{ab}{a+b}} \\ b=9+{\displaystyle \frac{ab}{a+b}} \\ {a}^2=4(a+b) \\ {b}^2=9(a+b) \\ a>0;b>0 \\ a=10 \\ b=15 \\ s=6 \end{gathered}$$

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